Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 256

9
=

cot A 1 ﾼ tan u 2 cos u 1 csc ʻ sin u 1 cot ʻ

ʻ
cos u 1 tan u 2

sin

, ð 5 : 112 Þ

tan A 1 ﾼ

;

sin u 1 cos ʻ

9
=
; :

cot A 2 ﾼ sin u 2 cot ʻ tan u 1 cos u 2 csc ʻ

sin ʻ

ð 5 : 113 Þ

tan A 2 ﾼ

sin u 2 cos ʻ tan u 1 cos u 2

Convert the Spherical Elements into Ellipsoidal Elements

1. Geodetic azimuths A 1 and A 2 remain unconverted.
2. Convert

˃ into S

S is given by:

1
ʱ ˃ ʲ

S ﾼ ﾽ sin ˃ cos 2M ð þ ˃ Þ ʳ sin 2 ˃ cos 4M ð þ 2 ˃ Þ , ð 5 : 114 Þ

where ʱ, ʲ, and ʳ are calculated according to the precise solution formula. The
accuracy required is the same as in the direct solution.

Determination of the Quadrant

In computation we also need to determine the quadrants of A 1 and A 2 . No more
details will be given here; see Table 5.9 .

Example

Block Diagram

The block diagram of computation for the solution of the inverse geodetic problem
is given in Fig. 5.49 .

Computations

Table 5.11 provides a sample computation for the solution of the inverse geodetic
problem.